Large‐scale covariate‐assisted two‐sample inference under dependence

The problems of large‐scale two‐sample inference often arise from the statistical analysis of “high throughput" data. Conventional multiple testing procedures usually suffer from loss of testing efficiency when conducting two‐sample t$$ t $$ ‐tests directly. To some extent, this is because of the ignorance of sparsity information. Moreover, the two‐sample tests commonly have local correlations, and neglecting the dependence structure may decrease the statistical accuracy. Therefore, it is imperative to develop a procedure that considers both sparsity information and dependence structure among the tests. We start by introducing a novel dependence model to allow for sparsity information and dependence structure. Based on the dependence model, we propose a covariate‐assisted local index of significance (COALIS)$$ \left(\mathbf{COALIS}\right) $$ procedure and show that it is valid and optimal. Then a data‐driven procedure is developed to mimic the oracle procedure. Both simulations and real data analysis show that the COALIS procedure outperforms its competitors.